$3.(20$ marks$)$ a$)$ You get a mortgage of $$100,000$ from the bank at an $8\mathrm{.}5\%$ annual interest rate to start your new business. The terms require you to amortize the loan with $10$ equal end$-$of$-$year payments. What is the ending balance of the $2$nd year? $(10$ marks$)$ b $)$ What's the present value of a $4-$year ordinary annuity of $$2,250$ per year plus an additional $$3,000$ at the end of Year $4$ if the interest rate is $5\%?(5$ marks$)$ c$)$ What is the present value of an investment with the following cash flows: Year $1$ : $$1,500$ Year $2$ : $$1,850$ Year $3$ : $$2,100$ Year $4$ : $$2,500$ Year $5$ : $$2,950$ Interest rate: